This is how I would represent the processing described by the OP:
"MAF8" represents a moving average filter over 8 samples. Even though the OP is doing a block average, the result will be identical to a moving average since the down-sample by 8 (which is shown by the down arrow with the 8 as typically done) will select each 8th sample resulting in the functionally equivalent processing.
The subsequent accumulation with a gain coefficient $\alpha$ at the lower rate at the output of the down-sample is drawn as traditionally done (with $\alpha <1$ to be stable, this is called a "leaky accumulator").
The depiction as a moving average makes understanding the spectrum of the filtering very straightforward. Prior to the down-sample, this will have a frequency response given as an "aliased Sinc function" or specifically the Dirichlet Kernel as given in the plot below and found from Matlab/Octave using:
freqz([1 1 1 1 1 1 1 1])
The OP is correct that the subsequent decimation is non-linear, and specifically results in aliasing of this frequency response. What I typically do is plot the frequency response using the above result out to the new digital frequency range (which is 1/8 of this spectrum) and then roll the remaining response to show the aliasing that would result from each of the upper frequency bands. This is shown below for the above frequency response from the moving average filter after the aliasing due to the down-sampling operation. What we see is the top blue curve represents the actual response for any signal that was originally in the band from DC to 1/16 of the original sampling rate (what becomes $f_s/2$ after down-sampling). The remaining curves are the attenuation for any signals at the higher frequencies that would alias into this band due to the down-sampling. Note we are seeing the mapping of the frequency response from the first curve cyclically folding onto the primary frequency band after down-sampling.
This process is then cascaded with the accumulator which has a frequency response (at the lower sampling rate) given by
$$H(z) = \frac{z}{z-\alpha}$$
For example with $\alpha=0.2$:
freqz(1, [1 -.2])
I would multiply the above response with the primary response given by the upper blue curve for the moving average filter and down-sampler to get the composite frequency response and I would take the aliasing curves as advise in terms of determining if there is sufficient filtering in these frequency bands prior to the down-sampling (there could be additional filtering ahead of this operation for example, or perhaps the possible interference is not of sufficient concern).
